What is sqrt(28+10\sqrt{3)} ?

The solution to sqrt(28+10\sqrt{3)} is sqrt(3)+5

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Popular >

simplify sqrt(28+10\sqrt{3)}

simplify

28 + 103

3 + 5

Decimal Notation

6.73205 \dots

Solution steps

28 + 103

= 3 + 103 + 25

= (3)^{2} + 103 + (25)^{2}

25 = 5

= (3)^{2} + 103 + 5^{2}

23 \cdot 5 = 103

= (3)^{2} + 23 \cdot 5 + 5^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(3)^{2} + 23 \cdot 5 + 5^{2} = (3 + 5)^{2}

= (3 + 5)^{2}

Apply radical rule:

(3 + 5)^{2} = 3 + 5

= 3 + 5

0.0196

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\frac{2 - 4 i}{i}